A127182 Number of distinct characteristic polynomials of n X n real robust {0,1}-matrices.

1, 2, 12, 156, 5612

Offset

1,2

Links

Table of n, a(n) for n=1..5.

Example

a(2)=2 because there are 4 binary robust 2 X 2 matrices, but only two distinct characteristic polynomials, namely y^2-y-1 and y^2-2y+1.
a(3)=12 because there are 12 different characteristic polynomials: -1-3y-y^2+y^3, 1-2y-y^2+y^3, 1+y-3y^2+y^3, -2+3y-3y^2+y^3, -1-2y-y^2+y^3, -1-y-y^2+y^3, -1+y-2y^2+y^3, 2-y-2y^2+y^3, -1+2y-3y^2+y^3, 1-y-2y^2+y^3, 1- 2y^2+y^3, -1+3y-3y^2+y^3.

Mathematica

mats[1] = {{{1}}}; mats[n_Integer?Positive] := mats[n] = Module[{newrows = Rest[Tuples[{0, 1}, {n}]], mp1 = Flatten[Function[k, Thread[(Append[ #1, #2]&)[ #1, k]]& /@ mats[n - 1]] /@ Tuples[{0, 1}, {n - 1}], 1]}, Flatten[MapThread[Function[{m, nl}, Append[m, # ]& /@ nl], {mp1, Pick[newrows, # =!= 0& /@ # ]& /@ (First /@ Dot[NullSpace /@ mp1, Transpose[newrows]])}], 1]] A127182[n_]=Length[Union[CharacteristicPolynomial[mats[n]]]]

Crossrefs

Cf. A125587, A125593, A127183, A127184, A127186.

Sequence in context: A366203 A130529 A075631 * A330552 A326222 A208577

Adjacent sequences: A127179 A127180 A127181 * A127183 A127184 A127185

Keyword

nonn

Author

Artur Jasinski and Peter Pein (petsie(AT)dordos.net), Jan 07 2007

Status

approved